Question: Multiply the following complex numbers: $({-5}) \cdot ({5-4i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-5}) \cdot ({5-4i}) = $ $ ({-5} \cdot {5}) + ({-5} \cdot {-4}i) + ({0}i \cdot {5}) + ({0}i \cdot {-4}i) $ Then simplify the terms: $ (-25) + (20i) + (0i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -25 + (20 + 0)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -25 + (20 + 0)i - 0 $ The result is simplified: $ (-25 - 0) + (20i) = -25+20i $